According to Horowitz and Marolf (HM) [1]}, the singular character of the spacetime is defined as the ambiguity in
the evolution of the wave functions. That is to say, the singular character
is determined based on the number of self-adjoint extensions of the
evolution operator to the entire Hilbert space. If the extension is unique, it is said
that the spacetime is quantum mechanically regular. The brief review of the method follows:
